Linked Questions

4
votes
6answers
3k views

Is H=H* sloppy notation or really just incorrect, for Hermitian operators?

I saw it in this pdf, where they state that $P=P^\dagger$ and thus $P$ is hermitian. I find this notation confusing, because an operator A is Hermitian if $\langle \Psi | A \Psi \rangle=\langle A \...
6
votes
2answers
2k views

Existence of adjoint of an antilinear operator, time reversal

The time reversal operator $T$ is an antiunitary operator, and I saw $T^\dagger$ in many places (for example when some guy is doing a "time reversal" $THT^\dagger$), but I wonder if there is a well-...
4
votes
3answers
934 views

Dirac notation - specific acting orientation for operators

I have this doubt: Imagine two operators $A$ and $B$ and the state $\psi$. I know that the following statement is true: $$\langle\psi| A|\psi\rangle^*=\langle\psi| A^\dagger|\psi\rangle$$ But is ...
4
votes
2answers
1k views

Adjoint of a Wave Function

Why is the adjoint of a function simply it's complex conjugate? Normally with a vector we consider the adjoint to be the transpose (And the conjugate? I don't know why), so does this concept carry ...
2
votes
3answers
487 views

How do you show that momentum is hermitian in Dirac notation?

I am trying to prove that momentum operator $\bf{\hat{p}}$ is hermitian. I know how to prove it in the $\bf{x}$ representation integrating by parts and using the fact that $\lim_{r \rightarrow \infty} ...
0
votes
1answer
385 views

What is the adjoint of a ket-bra?

Let $T$ be a linear operator, then we can consider the rank-one operator $$\vert Tx \rangle \langle y \vert.$$ I am wondering what is its adjoint operator, is it $$\vert y \rangle \langle T^*x \...
0
votes
2answers
469 views

How to prove this identity for the complex conjugate of linear operator?

I want to prove the following identity: $$\langle v|\Omega^{\dagger}|u\rangle = \langle u|\Omega | v \rangle^*$$ How should I go about this? I believe I can prove it when $\Omega$ is hermitian, but ...
-1
votes
1answer
237 views

Property of the adjoint operator in the array element

In Quantum Mechanics how can I prove this property? $$<\psi|A^{\dagger} |\phi>=<\phi|A|\psi>^{*}$$
2
votes
1answer
164 views

Notation doubt - inner product

I have a notational problem, I know when you define bra and ket you are defining an inner product, but you can see it as an linear operation where the linear operators (bras) act on vectors (kets), ...
0
votes
2answers
65 views

Associative product of two Anti-Linear(/Unitary) Operator

An operator is said to be linear if it obeys the distributive law and commutes with the constant i.e. $\hat{A}(a_1 |\psi_1\rangle + a_2|\psi_2\rangle)=a_1\hat{A}|\psi_1\rangle +a_2\hat{A}|\psi_2\...
0
votes
2answers
93 views

Dirac expression derivation

In Quantum Mechanics, 2nd Edition by Davies & Betts on page 78 it states that there is a symmetry implied by the following Hermitian operator equation: $${\displaystyle \int \phi^{*}(A \psi)d \,\...